Results 31 to 40 of about 403 (167)

Integrated Jacobi elliptic function solutions to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation by utilizing new solutions of the elliptic equation of order six

Partial Differential Equations in Applied Mathematics
In this research, the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation ((3+1)-GKPE) that expresses various nonlinear phenomena was studied.
Ahmad H. Alkasasbeh, Belal Al-Khamaiseh, Ahmad T. Ali   +2 more
doaj   +1 more source

New Exact Jacobi Elliptic Function Solutions for the Coupled Schrödinger-Boussinesq Equations

Journal of Applied Mathematics, 2013
A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic computation is proposed to construct ...
Baojian Hong, Dianchen Lu
doaj   +1 more source

A Novel Approach to a Time-Dependent-Coefficient WBK System: Doubly Periodic Waves and Singular Nonlinear Dynamics

Complexity, 2018
Under investigation in this paper is a more general time-dependent-coefficient Whitham-Broer-Kaup (tdcWBK) system, which includes some important models as special cases, such as the approximate equations for long water waves, the WBK equations in shallow
Bo Xu, Sheng Zhang
doaj   +1 more source

The Analytical Fractional Solutions for Coupled Fokas System in Fiber Optics Using Different Methods

Fractal and Fractional, 2023
The Fokas system with M-truncated derivative (FS-MTD) was considered in this study. To get analytical solutions of FS-MTD in the forms of elliptic, rational, hyperbolic, and trigonometric functions, we employed the extend F-expansion approach and the ...
Wael W. Mohammed, Clemente Cesarano, Elsayed M. Elsayed, Farah M. Al-Askar   +3 more
doaj   +1 more source

Differentiable Randers‐Finsler Eikonal Solvers

Computer Graphics Forum, EarlyView.
Abstract Fast and differentiable solvers for anisotropic and asymmetric distance fields are a key primitive in geometry processing, enabling gradient‐based optimization over metrics, drift fields, and downstream objectives that depend on geodesic distances and geodesics.
Barak Gahtan, Jacob Shpund, Alex M. Bronstein   +2 more
wiley   +1 more source

Jacobi elliptic function expansion method applied to long-short wave interaction equations

Acta Physica Sinica, 2003
In this paper,the Jacobi elliptic function method is generalized to study nonlinear evolution system. The envelope periodic solutions of long-short wave interaction equation are obtained. The solitary wave solutions for this model are also given under some conditions.
null Guo Guan-Ping, null Zhang Jie-Fang
openaire   +1 more source

The Long Shadow of Karl Weierstraß Over the Calculus of Variations

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT At first glance, it appears that the contents of Karl Weierstraß's (1815–1897) lecture courses on the calculus of variations were made available to the public only in the seventh volume of his Mathematische Werke, and thus not until 30 years after his death.
Peter Ullrich
wiley   +1 more source

Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation

Scientific Reports, 2023
In this research, we investigate the integrability properties of the Schamel–Korteweg–de Vries (S-KdV) equation, which is important for understanding the effect of electron trapping in the nonlinear interaction of ion-acoustic waves.
A. Hussain, Younes Chahlaoui, M. Usman, F. D. Zaman, Choonkil Park   +4 more
doaj   +1 more source

EXPANSION METHOD ABOUT THE JACOBI ELLIPTIC FUNCTION ANDITS APPLICATIONS TO NONLINEAR WAVE EQUATIONS

Acta Physica Sinica, 2001
A Jacobi elliptic function expansion method is proposed to construct the exact periodic solutions of nonlinear wave equations. This new method contains the hyperbolic tangent expansion method, and the periodic solutions obtained by this method, include the shock wave solutions and the solitary wave solutions.
null LIU SHI-KUO, null FU ZUN-TAO, null LIU SHI-DA, null ZHAO QIANG   +3 more
openaire   +1 more source

Stochastic Galerkin and Monte Carlo Methods for Parabolic Problems: Numerical Performance of Variational Matrix‐Free Approximations

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.
ABSTRACT Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational discretizations of the space and time variables. Due to the high dimensionality, the solution of the arising algebraic systems do not become feasible without ...
Moataz Dawor, Nils Margenberg, Markus Bause   +2 more
wiley   +1 more source